Statistics and Probability
Core ideas
Statistics questions ask you to describe data and make comparisons. Know measures of center-mean, median, mode-and measures of spread such as range and interquartile range. The mean is sensitive to outliers; the median is resistant. Read scatter plots for association: positive, negative, or none, and linear or nonlinear. Correlation describes strength and direction of a linear relationship, not causation. A line of best fit models the trend and can be used for prediction within the data range. In probability, find the sample space and count favorable outcomes. For two-way tables, distinguish marginal, joint, and conditional probabilities; a conditional probability uses a row or column total as the denominator.
Traps
Do not confuse correlation with causation. When finding a conditional probability, do not divide by the grand total if the question restricts the group. For events with replacement, the denominator stays the same; without replacement, it decreases. A mean can be pulled far from the median by one extreme value, so “typical” may be better represented by the median. Do not extrapolate far beyond the data when using a trend line.
Worked example
In a class, 12 students play a sport and 8 do not. Of the 12 athletes, 5 also play an instrument. The probability that a student plays an instrument given that the student plays a sport is 5/12, not 5/20. Rule of thumb: “given that” tells you to restrict the denominator to that group.